12/10/2007, 04:11 AM

For more information about the Lambert W function, which this thread seems to be a great deal about, Wolfram's function website has a wealth of information about W and about the branches of W (you can even download PDFs of each section). To answer Ivars' question earlier in this thread, the method probably used to find the power series expansions of the Lambert W function is probably to apply general analytic continuation techniques, or to solve what coefficients satisfy the following differential equation:

as this uniquely defines the Lambert W function along with initial conditions.

The general series expansion of the Lambert W function for all branches is:

which can be obtained by repeated application of the derivative formula:

from which the differential equation came. So all you need is the starting value at the starting point and you can form a series expansion of W anywhere. These are just the formulas I found on Wolfram's function website.

Andrew Robbins

as this uniquely defines the Lambert W function along with initial conditions.

The general series expansion of the Lambert W function for all branches is:

which can be obtained by repeated application of the derivative formula:

from which the differential equation came. So all you need is the starting value at the starting point and you can form a series expansion of W anywhere. These are just the formulas I found on Wolfram's function website.

Andrew Robbins